Honestly, wraps in the stall every night with no compelling reason is more for us then them. We need to feel like we are doing something. Yeah, if they tend to stock up it will reduce that but so will walking them for 15 minutes the next morning. Wraps don’t really add significant support to the tendons, afford only a little superficial protection against minor scrapes and bruises and protect wounds and bandages. If he’s just going to pick them off and there’s no compelling reason to use them, why bother? He hates them anyway, it’s no reward for a good school for him, it’s an annoyance. Let him be.
I wrapped mine at shows because I got tired of defending my choice not to and, honestly, some of those road stalls were pretty sketchy so even a little protection seemed sensible. My trainers all wrapped at shows, matching wraps of course. But because it looked nice and was expected more then anything else, didn’t wrap at home at all.
I had one horse years ago that simply would not tolerate keg wraps. We tried everything, no go, he was up all night picking them off. Looked like he’d been up all night too.